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sequence

Source: 2009 HongKong mathematic Olympiad

February 11, 2012
algebra proposedalgebra

Problem Statement

let an{a_{n}} be a sequence of integers,a1a_{1} is odd,and for any positive integer nn,we have n(an+1−an+3)=an+1+an+3n(a_{n+1}-a_{n}+3)=a_{n+1}+a_{n}+3,in addition,we have 20102010 divides a2009a_{2009} find the smallest n≥ 2n\ge\ 2,so that 20102010 divides ana_{n}
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